Just specifically for the U.S., the question can be answered like this: the philosophic rationale was of social uplift. White Americans posited that, without slavery, black Africans would be savage, and not know civilization. The economic rationale really begins in the great engine of European imperialism with the use of African for labor in the labor-intensive plantation systems in the Americas. The U.S. needs inclusion into this model, for here the U.S--especially the American South--has its national genesis. Yet how white American southerners justified the system of slavery lay in their perceived disadvantages with the North. Some white elites actually believed that, without slavery, the South would have no economy, and without wealth, would be beholden to the North--almost like a colony. White northerners are not exempted, however. They too thought, that without American slavery, they would not have the labor for the raw materials to, first sell to Europe--and Englands burgeoning industries--, then, later, keep for themselves to furnish their own nascent factories, in order to compete with England, lest the American economy grow weak, and the U.S. too, become a colony, and with that, lose its liberty.

I would also that white Americans, north and south, saw an advantage of a laboring class that did not have political power, which philosophically supported the belief that a laboring poor weakened republicanism in a nation like the United States. Without a restive class that had political representation, late 18th Century racially-biased democracy could succeed.